Method and apparatus to generate an RF excitation consistent with a desired excitation profile using a transmit coil array

ABSTRACT

A system composed of multiple transmit coils with corresponding RF pulse synthesizers and amplifiers is disclosed. A method of designing RF pulses specific to each transmit coil to induce spatiotemporal variations in a composite B 1  field is also disclosed. The present invention supports faithful production of desired excitation profiles and accommodates the use of any coil array geometry. The present invention also supports reduction in excitation pulse length. Through effective B 1  field maps for each transmit coil, mutual coupling and other inter-coil correlations are accounted for in the RF pulse design.

BACKGROUND OF THE INVENTION

The present invention relates generally to MR imaging and, moreparticularly, to a method and apparatus of parallel excitation by atransmit coil array to realize a desired excitation profile. The presentinvention further relates to a parallel excitation pulse design methodthat accounts for mutual coupling between coils of the coil array andapplies to any coil geometry. The present invention is further directedto targeted RF excitation across an imaging volume to accelerate MRimaging.

When a substance such as human tissue is subjected to a uniform magneticfield (polarizing field B₀), the individual magnetic moments of thespins in the tissue attempt to align with this polarizing field, butprecess about it in random order at their characteristic Larmorfrequency. If the substance, or tissue, is subjected to a magnetic field(excitation field B₁) which is in the x-y plane and which is near theLarmor frequency, the net aligned moment, or “longitudinalmagnetization”, M_(Z), may be rotated, or “tipped”, into the x-y planeto produce a net transverse magnetic moment M_(t). A signal is emittedby the excited spins after the excitation signal B₁ is terminated andthis signal may be received and processed to form an image.

When utilizing these signals to produce images, magnetic field gradients(G_(x), G_(y), and G_(z)) are employed. Typically, the region to beimaged is scanned by a sequence of measurement cycles in which thesegradients vary according to the particular localization method beingused. The resulting set of received NMR signals are digitized andprocessed to reconstruct the image using one of many well knownreconstruction techniques.

Spatially selective excitation is widely used in MR imaging to inducetransverse magnetization while limiting the size of thesignal-contributing volume. Slice-selective excitation, the mostcommonly used, confines the signal-contributing volume to a fixed slicethat simplifies spatial encoding during signal acquisition to reducedata acquisition or scan time. Multi-dimensional excitation thatproduces localization along more than one dimension has been used tofurther this reduction in scan time. For example, localizedspectroscopy, reduced-FOV scan of a region of interest, imaging of atarget anatomy of unique shape, and echo planar imaging (EPI) with ashortened echo train length are applications usually implemented becauseof their support of reduced scan times. In addition, profile (flip,phase, and frequency) control across a sizeable volume with selectiveexcitation has been exploited to improve excitation profile fidelity inthe presence of B₀ inhomogeneity or gradient non-linearity, and toreduce susceptibility artifacts.

Selective excitation is commonly implemented with a single transmit coilthat transmits across an entire volume and produces a relatively uniformB₁ field, e.g., a birdcage coil. Highly efficient pulse algorithms havebeen developed for designing excitation pulses that suit such aconfiguration. Notwithstanding the advantages achieved by these pulsedesign tools, technical difficulties remain. Issues with excitationpulse duration, excitation profile accuracy, and RF power absorption(SAR) represent some of the outstanding challenges in a variety ofapplications. Compared to 1D excitation, flexible profile control alongmultiple dimensions with 2D or 3D excitation entails intensified pulsingactivity and often requires powerful gradients to keep pulse duration incheck. This limitation hinders applications of multi-dimensionalexcitation on scanners with general-purpose gradients. Substantialsubject-dependency of B₁ field, resulting from increased wave behaviorand source-subject interaction at high frequencies, may also contributeto the difficulty of excitation profile control. An elevated rate of RFpower deposition at high frequencies represents yet another factor thathas a significant impact on the design and application of RF transmitmodules and/or excitation pulses.

Use of adiabatic pulses represents a pulse design approach thataddresses the difficulty of excitation profile control associated withB₁ inhomogeneity. This approach is limited as its application has beenlimited to certain profiles and tends to involve high RF power. AB₁-field optimization approach that aims at maximizing global B₁homogeneity addresses the control issue through transmit moduleimprovements. Adaptation of the transmit coil geometry or the drivingmechanism has been shown to reduce B₁ inhomogeneity. At high frequencieshowever, the capability of a field optimization approach is limited.Even with calibration-guided adjustment of driving port weights, thedegree to which the spatial variation of the composite B₁ fieldapproaches a desired level is highly dependent on the characteristics ofcomponent B₁ fields, and results tend to be subject to considerableresidual inhomogeneity.

Another proposed solution to reduce excitation pulse length is based ona parallel excitation architecture—multiple transmit elements driven byindependent drivers. Individual B₁ field patterns are employed tosuppress aliasing lobes arising from sampling density reduction in theexcitation k-space. Notwithstanding the excitation pulse lengthreduction achieved with a parallel excitation structure, application ofsuch a structure has shown that particulars of the transmit elements arenot fully taken into account. That is, these known parallel transmitarchitectures fail to consider mutual coupling between transmit elementsand are often dependent upon a simplistic transmit array geometry. Assuch, spatial variations created by the transmit elements are not fullyexploited.

It would therefore be desirable to have a system and method capable ofrealizing desired excitation profiles and reducing excitation pulselength by the means of a parallel transmit element architecture, whereappropriate B₁ field spatiotemporal variations are effected in acomposite B₁ field created by a transmit coil array.

BRIEF DESCRIPTION OF THE INVENTION

The present invention provides a system and method of effectingspatiotemporal variations in a composite B₁ field created by a transmitcoil array that overcomes the aforementioned drawbacks.

The present invention is directed to the acceleration of amulti-dimensional excitation through the orchestrated driving ofmultiple transmit coils. The present invention emphasizes thecoordination of multiple transmit elements to effect appropriate B₁spatiotemporal variations in a composite B₁ field in order to improvethe management of multi-dimensional pulse length while facilitatingfaithful production of desired excitation profiles. The presentinvention is also directed to the design of parallel excitation pulseswith spatial and spatial-frequency domain weighting.

Therefore, in accordance with one aspect of the present invention, amethod is presented that includes the step of determining a desired RFexcitation profile. The method further includes the step ofindependently driving each transmit coil of a transmit coil array suchthat the result of a collective excitation generated by the transmitcoil array substantially matches the desired RF excitation profile.

In accordance with another aspect of the invention, an MRI apparatusincludes an MRI system having a magnet to impress a polarizing magneticfield and a plurality of gradient coils positioned about the bore of themagnet to impose a magnetic field gradient. An RF transceiver system andan RF switch are controlled by a pulse module to transmit and receive RFsignals to and from an RF coil assembly to acquire MR images. The MRIapparatus also includes a computer programmed to design a plurality ofRF pulse waveforms configured to control RF generation by a transmitcoil array such that the result of collective RF generation across animaging volume substantially matches a desired RF excitation profileindependent of transmit coil array geometry.

In accordance with another aspect of the invention, the invention isembodied in a computer program stored on a computer readable storagemedium and having instructions which, when executed by a computer, causethe computer to control RF transmission by a plurality of transmit coilsof a transmit coil array such that spatial and temporal variation in acomposite B₁ field, accompanied by appropriate gradient changes playedout in synchrony, create a desired excitation profile upon completion ofRF transmission.

Various other features, objects and advantages of the present inventionwill be made apparent from the following detailed description and thedrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings illustrate one preferred embodiment presently contemplatedfor carrying out the invention.

In the drawings:

FIG. 1 is a schematic block diagram of an MR imaging system for use withthe present invention.

FIG. 2 is a block diagram illustrating a linear transmit coil arrayassembly in accordance with one aspect of the present invention.

FIG. 3 is a block diagram illustrating a wrap-around transmit coil arrayassembly in accordance with another aspect of the present invention.

FIG. 4 is a graph illustrating an RF excitation profile achievable witha transmit coil array in accordance with the present invention.

FIGS. 5-6 are plots illustrating k_(x)-direction weighting contributionby the coils of a transmit coil array positioned at two x-axislocations.

FIG. 7 illustrates the magnitude of localization profiles along thex-axis for each coil of a transmit coil array.

FIG. 8 graphically illustrates a pulse sequence in accordance with oneaspect of the present invention.

FIG. 9 illustrates resulting 2D transverse magnetization distribution asestimated by removing coil sensitivity weighting from an acquired image.

FIG. 10 illustrates B₁ field maps for the coils of an exemplary transmitcoil array.

FIG. 11 illustrates transverse magnetization distribution from anon-selective excitation in a reference body coil.

FIG. 12 illustrates B₁ field maps for each coil of a transmit coil arrayas well as a composite field map generated by superimposing theindividual B₁ field maps.

FIGS. 13-16 illustrate results of an RF pulsing protocol to control RFtransmission and minimize RF deposition on a subject in accordance withanother aspect of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIG. 1, the major components of a preferred magneticresonance imaging (MRI) system 10 incorporating the present inventionare shown. The operation of the system is controlled from an operatorconsole 12 which includes a keyboard or other input device 13, a controlpanel 14, and a display screen 16. The console 12 communicates through alink 18 with a separate computer system 20 that enables an operator tocontrol the production and display of images on the display screen 16.The computer system 20 includes a number of modules which communicatewith each other through a backplane 20 a. These include an imageprocessor module 22, a CPU module 24 and a memory module 26, known inthe art as a frame buffer for storing image data arrays. The computersystem 20 is linked to disk storage 28 and tape drive 30 for storage ofimage data and programs, and communicates with a separate system control32 through a high speed serial link 34. The input device 13 can includea mouse, joystick, keyboard, track ball, touch activated screen, lightwand, voice control, or any similar or equivalent input device, and maybe used for interactive geometry prescription.

The system control 32 includes a set of modules connected together by abackplane 32 a. These include a CPU module 36 and a pulse generatormodule 38 which connects to the operator console 12 through a seriallink 40. It is through link 40 that the system control 32 receivescommands from the operator to indicate the scan sequence that is to beperformed. The pulse generator module 38 operates the system componentsto carry out the desired scan sequence and produces data which indicatesthe timing, strength and shape of the RF pulses produced, and the timingand length of the data acquisition window. The pulse generator module 38connects to a set of gradient amplifiers 42, to indicate the timing andshape of the gradient pulses that are produced during the scan. Thepulse generator module 38 can also receive patient data from aphysiological acquisition controller 44 that receives signals from anumber of different sensors connected to the patient, such as ECGsignals from electrodes attached to the patient. And finally, the pulsegenerator module 38 connects to a scan room interface circuit 46 whichreceives signals from various sensors associated with the condition ofthe patient and the magnet system. It is also through the scan roominterface circuit 46 that a patient positioning system 48 receivescommands to move the patient to the desired position for the scan.

The gradient waveforms produced by the pulse generator module 38 areapplied to the gradient amplifier system 42 having G_(x), G_(y), andG_(z) amplifiers. Each gradient amplifier excites a correspondingphysical gradient coil in a gradient coil assembly generally designated50 to produce the magnetic field gradients used for spatially encodingacquired signals. The gradient coil assembly 50 forms part of a magnetassembly 52 which includes a polarizing magnet 54 and a whole-body RFcoil 56. A transceiver module 58 in the system control 32 producespulses which are amplified by an RF amplifier 60 and coupled to the RFcoil 56 by a transmit/receive switch 62. The resulting signals emittedby the excited nuclei in the patient may be sensed by the same RF coil56 and coupled through the transmit/receive switch 62 to a preamplifier64. The amplified MR signals are demodulated, filtered, and digitized inthe receiver section of the transceiver 58. The transmit/receive switch62 is controlled by a signal from the pulse generator module 38 toelectrically connect the RF amplifier 60 to the coil 56 during thetransmit mode and to connect the preamplifier 64 to the coil 56 duringthe receive mode. The transmit/receive switch 62 can also enable aseparate RF coil (for example, a surface coil) to be used in either thetransmit or receive mode.

The MR signals picked up by the RF coil 56 are digitized by thetransceiver module 58 and transferred to a memory module 66 in thesystem control 32. A scan is complete when an array of raw k-space datahas been acquired in the memory module 66. This raw k-space data isrearranged into separate k-space data arrays for each image to bereconstructed, and each of these is input to an array processor 68 whichoperates to Fourier transform the data into an array of image data. Thisimage data is conveyed through the serial link 34 to the computer system20 where it is stored in memory, such as disk storage 28. In response tocommands received from the operator console 12, this image data may bearchived in long term storage, such as on the tape drive 30, or it maybe further processed by the image processor 22 and conveyed to theoperator console 12 and presented on the display 16.

The present invention is directed to a method and system of acceleratingRF pulse transmission by a plurality of transmit coils. Such a transmitcoil array is illustrated in FIG. 2. Transmit coil array assembly 70includes a plurality of RF coils or elements 72 that are designed forparallel RF transmission, and a plurality of RF amplifiers 74. In onepreferred embodiment, each transmit coil 72 is driven by a dedicated RFamplifier 74. In this regard, each RF amplifier is configured togenerate a controlled current in a respective RF coil for defining andsteering an excitation volume 76 of a subject 78 within an MRI system.As will also be described, each of the transmit coils is controlled in amanner such that inter-coil correlations, i.e. mutual coupling, aretaken into account. As illustrated in FIG. 2, the transmit coils 72 arearranged in a substantially linear fashion. Additionally, as will bedescribed in greater detail, the RF amplifiers drive the plurality of RFtransmit coils such that RF excitation may be substantially localized toa particular region-of-interest so as to reduce RF power deposition onthe subject. As will be further described, each of the transmit coils iscontrolled in a manner such that RF power deposition is further reduced.

Referring now to FIG. 3, transmit coil array assembly 70 is illustratedin another embodiment. In this embodiment, the transmit coils 72 arepositioned in a wrap-around manner. In this regard, the coils arearranged in a distributed manner around the subject. Similar to thatshown and described with respect to FIG. 2, each RF coil 72 is connectedto a dedicated RF amplifier 74. One skilled in the art will readilyappreciate that FIGS. 2-3 illustrate a pair of possible arrangements ofthe coils of a transmit coil array and that other arrangements notspecifically illustrated are possible and contemplated.

As indicated above, the present invention is directed to a method andsystem operable with a transmit coil array such that RF excitation bythe transmit coils is carried out in parallel. This parallel excitationsupports a reduction in scan time through the acceleration of RF pulsesand the localization of targeted excitation.

The present invention will be described with respect to asmall-tip-angle excitation, but one skilled in the art will appreciatethat the present invention is extendable to other excitation regimes.The transverse magnetization resulting from a small-tip-angle excitationwith a single transmit coil may be analyzed by the Fourier transform ofthe k-space trajectory traversed and weighted during the excitation:$\begin{matrix}{{{M(x)} = {j\quad\gamma\quad{M_{0}(x)}{b(x)}{\int_{x}{{W(k)}{S(k)}{\mathbb{e}}^{j\quad 2\quad\pi\quad{k \cdot x}}{\mathbb{d}k}}}}},} & {{Eqn}.\quad 1}\end{matrix}$where S(k) represents a spatial-frequency sampling trajectory controlledby the switching gradients, W(k), a spatial-frequency weighting inducedby the driving RF source, and b(x), a spatial weighting induced by thecoil's B₁ field pattern.

When several sets of pulse synthesizers and amplifiers form parallel RFsources that simultaneously drive corresponding coils during excitation,multiple spatial-frequency and spatial weightings influence the creationof the transverse magnetization. Within the limits of thesmall-tip-angle approximation, the k-space perspective expressed by Eqn.1 may be extended to analyze a parallel excitation system based on theproperty of linearity: $\begin{matrix}{{M(x)} = {j\quad\gamma\quad{M_{0}(x)}{\sum\limits_{n = 1}^{N}{{b_{n}(x)}{\int_{k}{\sum\limits_{l = 1}^{N}{c_{n,l}{W_{l}(k)}{S(k)}{\mathbb{e}}^{j\quad 2\quad\pi\quad{k \cdot x}}{{\mathbb{d}k}.}}}}}}}} & {{Eqn}.\quad 2}\end{matrix}$In Eqn. 2, N denotes the total number of transmit coils, n and l arecoil indices, c_(n,l) are coefficients characterizing the mutualcoupling between the coils, W_(l)(k) represent spatial-frequencyweightings induced by the independently controlled RF sources, andb_(n)(x) represent spatial weightings induced by the coils respective B₁field patterns.

With g(x) denoting the term in Eqn. 2 that defines the excitationprofile, g(x) may be expressed as $\begin{matrix}{{g(x)} = {\sum\limits_{l = 1}^{N}{\left( {\sum\limits_{n = 1}^{N}{c_{n,l}{b_{n}(x)}}} \right){\int_{k}{{W_{l}(k)}{S(k)}{\mathbb{e}}^{j\quad 2\quad\pi\quad{k \cdot x}}{\mathbb{d}k}}}}}} & {{Eqn}.\quad 3} \\{\quad{{= {\sum\limits_{l = 1}^{N}{{{\hat{b}}_{l}(x)}{\int_{k}{{W_{l}(k)}{S(k)}{\mathbb{e}}^{j\quad 2\quad\pi\quad{k \cdot x}}{\mathbb{d}k}}}}}},}} & \quad\end{matrix}$which indicates that in the analysis of the parallel transmit system,${{{\hat{b}}_{l}(x)} \equiv {\sum\limits_{n = 1}^{N}{c_{n,l}{b_{n}(x)}}}},$the effective spatial weightings, may be used to account forcoupling-induced inter-coil correlations.

As an example, a 2D excitation case is considered, where an echo planar(k_(x),k_(y)) trajectory, with k_(x) being the slow direction and Δ_(kx)being the sampling period, is used and {(x,y)|x_(min)≦x≦x_(max),y_(min)≦y≦y_(max)} specifies the field-of-view that contains thesubject. The k-space weighting and sampling gives rise to a 2Dexcitation profile, which, as defined by Eqn. 3, is a weightedsuperposition of N periodic functions: $\begin{matrix}{{g\left( {x,y} \right)} = {\sum\limits_{l = 1}^{N}{{{\hat{b}}_{l}\left( {x,y} \right)}{\sum\limits_{m = {- \infty}}^{+ \infty}{{u_{l}\left( {{x - {m\quad\Delta}},y} \right)}.}}}}} & {{Eqn}.\quad 4}\end{matrix}$In Eqn. 4, the notation u_(l)(x) and Δ represent, respectively,∫W_(l)(k)e^(j2πk·x)dk and 1/Δ_(kx). Z-dependence has been suppressed forsimplicity.

From Eqn. 4, it is clear that the discrete nature along k_(x)necessarily implies aliasing lobes along x. Of significance, Eqn. 4indicates that side lobe suppression may be achieved through multipleweighting in the spatial ({circumflex over (b)}_(l)(x)) andspatial-frequency (W_(l)(k)) domains. This can be compared to the caseof excitation with a body-coil (volume coil with b(x)≈1), where atypical pulse design has the side lobes pushed outside the subject bylimiting sampling period Δ_(kx) to be no greater than 1/D(D=x_(max)−x_(min)).

Within a small-tip-angle regime, design of gradient and RF pulses givena desired excitation profile may be achieved solving an inverse problemdefined by Eqn. 3. For the purpose of illustration, a 2D excitation willbe described.

To achieve a 2D excitation profile given by g(x,y) and with solutions oftype: u_(l)(x,y)=h_(l)(x,y)g(x,y), Eqn. 4 may be rewritten as:$\begin{matrix}{{{g\left( {x,y} \right)} = {\sum\limits_{m = {- \infty}}^{+ \infty}{{g\left( {{x - {m\quad\Delta}},y} \right)}{\sum\limits_{l = 1}^{N}{{h_{l}\left( {{x - {m\quad\Delta}},y} \right)}{{\hat{b}}_{l}\left( {x,y} \right)}}}}}},} & {{Eqn}.\quad 5}\end{matrix}$which in general requires, for all (x,y) inside the field-of-view,$\begin{matrix}{{\sum\limits_{l = 1}^{N}{{h_{l}\left( {{x - {m\quad\Delta}},y} \right)}{{\hat{b}}_{l}\left( {x,y} \right)}}} = \left\{ {\begin{matrix}{1,} & {m = 0} \\{0,} & {otherwise}\end{matrix}.} \right.} & {{Eqn}.\quad 6}\end{matrix}$

By sorting the equations (e.g., through change of variables), it can beshown that {h_(l)(x,y), l=1, . . . , N} is typically constrained, ateach (x,y), by K linear equations (K is defined as the smallest integerthat is greater or equal to D/Δ):C _((x,y)) h _((x,y)) =e ₁  Eqn. 7,where $\begin{matrix}{{C_{({x,y})} = \begin{bmatrix}{{\hat{b}}_{1}\left( {x,y} \right)} & {{\hat{b}}_{2}\left( {x,y} \right)} & \cdots & {{\hat{b}}_{N}\left( {x,y} \right)} \\\vdots & \vdots & \quad & \vdots \\{{\hat{b}}_{1}\left( {{x + {m\quad\Delta}},y} \right)} & {{\hat{b}}_{2}\left( {{x + {m\quad\Delta}},y} \right)} & \cdots & {{\hat{b}}_{N}\left( {{x + {m\quad\Delta}},y} \right)} \\\vdots & \vdots & \quad & \vdots\end{bmatrix}},} & {{Eqn}.\quad 8}\end{matrix}$  h _((x,y)) =[h ₁(x,y) h ₂(x,y) . . . h_(N)(x,y)]^(T)  Eqn. 9,e₁=[1 0 . . . 0]^(T)  Eqn. 10,and {x, . . . , x+mΔ (m≠0), . . . } represents the set of x coordinateswithin the field-of-view that are evenly spaced and inter-associated dueto aliasing. Employing a sampling period Δ_(kx) that is greater than1/D, all but the first equation in Eqn. 7 represent the suppression ofaliasing side lobes located within the field-of-view.

Solving Eqn. 7 repeatedly for locations throughout the field-of-viewyields h_(l)(x,y)'s, which then allow the calculation of k-spaceweighting according to the following: $\begin{matrix}{{W_{l}(k)} = {\int_{x}{{h_{l}(x)}{g(x)}{\mathbb{e}}^{{- j}\quad 2\quad\pi\quad{k \cdot x}}{{\mathbb{d}x}.}}}} & {{Eqn}.\quad 11}\end{matrix}$The k-space weighting, and the RF pulse waveform associated with the Ithcoil, can thus be calculated with the Fourier transform of aspatially-weighted version of the desired excitation profile, where thespatial weighting is derived from B₁ field maps of each transmit coiland the k-space traversing trajectory.

Quality of B₁ field maps has a direct impact on excitation profileaccuracy. The maps may be experimentally calibrated one at a time. Withthis approach, each calibration may involve an imaging experiment thatuses a single element of the transmit array for transmission (with zeroinputs to other elements) and the body coil for reception. A division ofthe result by a reference image for removing the modulation of subjectcontrast and additional processing for suppressing the effects of noise,then provides an estimate of the effective B₁ map associated with thetransmit element. Alternatively, B₁ maps may be inferred fromsensitivity maps based on the principle of reciprocity. It should benoted that multiple sensitivity maps may be calibrated in parallel toreduce calibration time. However, the opposite phase and possiblechanges in coil coupling characteristics between transmit and receive,if not accounted for, may compromise the accuracy of the estimatedeffective B₁ maps.

Comparing two types of systems in the 2D excitation example, the presentinvention provides excitation acceleration of up to N-fold over asingle-channel body-coil system. Formally, this is revealed by the factthat Eqn. 7 admits at least one solution if N≧D/Δ, or equivalently,Δ_(kx)≦N/D, which is in contrast to the more stringent requirement ofΔ_(kx)≦1/D in the case of body-coil transmission. Intuitively, thecapacity for acceleration, or, reduction in excitation k-space samplingdensity, is probably best appreciated by recognizing that while areduction in excitation k-space sampling density causes aliasing lobesto locate inside the subject, an appropriate design of thespatial-frequency domain weighting (W_(l)(k)) can combine with thespatial domain weighting ({circumflex over (b)}_(l)(x)) and the aliasingpattern (as determined by the sampling) to cause incoherent addition,therefore realizing reduction or annihilation of aliasing lobes' netamplitudes.

For an acceleration factor that is smaller than N, or equivalently, asampling period that is smaller than N/D, Eqn. 7 allows a family ofsolutions of dimensionality N−K. This results in choices of excitationpulse designs that are all capable of producing a main lobe that matchesthe desired excitation profile and, when applicable, simultaneouslysuppressing aliasing lobes. The specific design that uses h_(l)(x,y)'scalculated by solving Eqn. 7 in the minimum norm sense is notable sinceit tends to lessen the sensitivity of the excitation profile toperturbations or reduces the power requirement on the RF amplifiers.

The independent driving of transmit coils of a transmit coil array alsosupports SAR management. Compared to uniform coverage of a subjectvolume with a single transmit coil, focused excitation of only theregion-of-interest with an array of distributed local transmit coils byemploying the coils in close proximity prevents substantial RF powerdeposition beyond the region. In addition, from the many ways oforchestrating the sources and achieving a desired excitation profile,the one that induces an E field with as small as possible an ensuing RFpower deposition can be chosen.

While the present invention supports a number of SAR reductiontechniques, i.e. focused RF excitation, SAR management with a focus onthe minimization of SAR averaged over the subject volume and theexcitation period, which is defined by: $\begin{matrix}{{{SAR}_{ave} = {\frac{1}{P}{\sum\limits_{p = 0}^{P - 1}{\frac{1}{V}{\int{\frac{\sigma(x)}{2\quad{\rho(x)}}{{E\left( {x,{p\quad\Delta\quad t}} \right)}}^{2}{\mathbb{d}v}}}}}}},} & {{Eqn}.\quad 12}\end{matrix}$will be hereinafter described in greater detail. In Eqn. 12, σ denotestissue conductivity; ρ, density; V, the size of the irradiated subjectvolume; and P, the total number of time points used to quantify thetemporal average.

Given, for example, multiple loop coils placed facing the surface of alarge slab of conducting material. At low frequencies, the fields insidethe slab tend to be dominated by the incident fields, which are producedby the currents in the coils. Following a quasi-static approach inanalyzing electric and magnetic near-fields, the fields may becharacterized with a vector potential A: $\begin{matrix}{{A = {\sum\limits_{l = 1}^{N}{\frac{\mu\quad I_{l}}{4\pi}{\oint\limits_{C_{l}^{\prime}}\frac{\mathbb{d}s^{\prime}}{\left| {x - x^{\prime}} \right|}}}}},} & {{Eqn}.\quad 13}\end{matrix}$where the line integrals over the currents in the coils are based onfilament approximation of the coil conductors, and the fields arerelated to A by B=∇×A and E=−dA/dt. In this case, the |E(x,pΔt)|² termin Eqn. 12 may be evaluated as: $\begin{matrix}\begin{matrix}{\left| {E\left( {x,{p\quad\Delta\quad t}} \right)} \right|^{2} = \left| {{- j}\quad\omega\quad{A\left( {x,{p\quad\Delta\quad t}} \right)}^{2}} \right.} \\{= \left| {\sum\limits_{l = 1}^{N}{{I_{l}\left( {p\quad\Delta\quad t} \right)}\left( {\frac{{- j}\quad\omega\quad\mu}{4\pi}{\oint\limits_{C_{l}^{\prime}}\frac{\mathbb{d}s^{\prime}}{\left| {x - x^{\prime}} \right|}}} \right)}} \right|^{2}} \\{{= \left| {\sum\limits_{l = 1}^{N}{{I_{l}\left( {p\quad\Delta\quad t} \right)}{\Phi_{l}(x)}}} \right|^{2}},}\end{matrix} & {{Eqn}.\quad 14}\end{matrix}$which is a quadratic form in [I_(l)(pΔt) I₂(pΔt) . . . I_(N)(pΔt)], avector with values of the current waveforms at time pΔt. Sorting out thevolume integral and temporal summation, SAR_(ave) may be expressed as aquadratic function in the samples of the current waveforms:SAR _(ave) =S ^(H) Fs  Eqn. 15,where superscript H denotes conjugate transpose, matrix F carriesentries evaluated based on Eqns. 12 and 14, and vector s collects in acorresponding order a total of N×P samples of the current waveforms.

Provided that the electric field scales linearly with applied sourcefunctions, a quadratic relationship in the form of Eqn. 5 betweenaverage SAR and source function samples generally holds. In the presenceof biological objects or at high frequencies however, solving Maxwell'sequations is difficult and construction of the F matrix may need to relyon calibration results or direct E field measurements.

Given the dependencies of the absorption rate and transversemagnetization on the applied source functions, the determination of aset of coordinated source functions that produces the desired excitationprofile while inducing minimum SAR is possible. In the small tip angleregime or its extension where a linear treatment of the Bloch equationsis appropriate, closed-form solution exists for multi-dimensionalexcitation design, which obviates the task of searching a vast designspace.

Continuing with the previously described 2D excitation example,equations of the form of Eqn. 7, which stem from the requirement ofcreating the desired main lobe in the subject while avoiding aliasinglobes, collectively constrain the spatial patterns of h_(l)(x)'s.Pooling these equations together thus gives the design constraints,which, in a matrix form, may be expressed as:C _(all) h _(all) =e _(all)  Eqn. 16.In Eqn. 16, C_(all) is a block-diagonal matrix with C_((x,y))'s on thediagonal and zeros everywhere else, and h_(all) and e_(all) are vectorsrepresenting, respectively, concatenated h_((x,y))'s and e₁'s. If amoving sample of the weighting functions is carried out at a constantrate, the W_(l)(k(t))'s are proportional to the current waveforms. TheFourier transform relationship between the W_(l)(k)'s and the h_(l)(x)'sallows rewriting Eqn. 15 in terms of h_(all):SAR _(ave) =h _(all) ^(H) Vh _(all)  Eqn. 17.The quadratic form remains as Fourier transform defines a linear mappingfrom h_(l)(x) to W_(l)(k). A variable sample rate would only modifyentries of matrix V to match gradient amplitude changes. As such, pulsedesign for SAR management may be achieved by minimizing a quadraticfunction subject to a linear constraint:minimize h_(all) ^(H)Vh_(all)subject to C _(all) h _(all) =e _(all)  Eqn. 18,which may be solved using well-known numerical techniques.

Design principles for small-tip-angle parallel excitation pulses such asthat described above were evaluated in simulation and phantomexperiments. To evaluate the design principle for acceleratedmulti-dimensional excitation, parallel excitation with a transmit coilarray was first examined in a simulation study. The transmit array wascomprised of nine identical 19.8 cm×6.4 cm loop coils that were placedon a flat form and lined up along the x-direction. This array faced athin slab object below the array surface. 2D excitation with a desiredexcitation profile across the object in the form ofg(x)=g_(x)(x)·g_(z)(z) was approached with parallel excitation pulses.In this case, use of an echo planar k_(x)-k_(z) trajectory consisting ofk_(x)=constant lines evenly spaced by Δ_(kx), the negligible y- andz-direction B₁ variation in the localized volume, and the separabilityof g(x) yielded solutions to Eqn. 11 of the formW_(l)(k)=U_(kx,l)(k_(x))·U_(kz)(k_(z)), where $\begin{matrix}{{U_{{kx},l}\left( k_{x} \right)} = {\int_{x}{{h_{l}(x)}{g_{x}(x)}{\mathbb{e}}^{{- j}\quad 2\quad\pi\quad{xk}_{x}}{\mathbb{d}x}}}} \\{{U_{kz}\left( k_{z} \right)} = {\int_{z}{{g_{z}(z)}{\mathbb{e}}^{{- {j2}}\quad\pi\quad{zk}_{z}}{\mathbb{d}z}}}}\end{matrix}.$For purposes of this first experiment equations of form Eqn. 7 wereconstructed and weightings over k_(x)-k_(z) were determined. RF pulsewaveforms were then calculated based on Eqn. 11. As a reference,body-coil excitation pulses aimed at the same 2D localization weredesigned.

The design principle for accelerated excitation was further evaluated ina phantom study, which was carried out on a 1.5 Tesla MRI scanner (CVi,GE Medical Systems, Waukesha, Wis.) with a setup very similar to that ofthe simulation study noted above. The transmit coil array of interestwas of the same geometry and placed 3 cm above a water-filled 41×19×1cm³ brick phantom. As the scanner only supported single-channel RF pulsetransmission, the study examined parallel excitation indirectly, bymimicking simultaneous driving of the nine array elements through aseries of nine single-channel experiments. Validity of the approach isensured by the property of linearity in the small-tip-angle regime,which allows the prediction of the result of a parallel excitationexperiment from the superposition of transverse magnetizationdistributions observed from single-channel excitation experiments.

Specifically, a single transmit/receive loop coil of size 19.8 cm×6.4 cmwas attached to the scanner's RF interface. During the nine experiments,the coil was placed and driven one configuration at a time, each with aposition and RF pulse corresponding to one of the nine elements on thevirtual coil array that were desired to simulate. After completion ofevery transmission, the coil was immediately switched to the receivefunction, whereas throughout the experiments the scanner's body coil waskept detuned. 2D excitation and acquisition were carried out with agradient echo sequence. From one experiment to another, excitationk-space traversing was kept the same (i.e., echo planar k_(x)-k_(z)trajectory with k_(x) being the slow direction) but the weighting (RFpulse) was changed according to the excitation pulse design. 2Dacquisition produced images that mapped out the water phantom along thex and z directions (and projected along y, the normal direction of the 1cm slab). 2D transverse magnetization distributions were quantified byremoving the coils' sensitivity profiles from the images. Thedistributions were then superimposed to provide an estimate of thedistribution resulting from the corresponding parallel excitationexperiment. By the design of the study, coil coupling is not a factor.B₁ maps that were estimated based on Biot-Savart Law were used in boththe RF pulse calculations and the sensitivity profile removal.

In another study on excitation acceleration, an all-around arraygeometry was examined. The array consisted of seven transmit elementsthat were distributed azimuthally on a wrap-around form inside ascanner's patient bore. Computer simulations evaluated 2D excitationdesigns that localize along both x and y dimensions. Coupling betweenelements was not negligible and was taken into account with a couplingmatrix determined from mutual inductance calculations. The designs usedthe original Eqns. 7 and 11.

Effectiveness of the SAR management scheme described previously asintegrated in the parallel pulse design was further evaluated. Theevaluation was carried out in the same fashion as the first simulationstudy except for the application of parallel excitation pulses of designtype defined by Eqn. 18 instead of Eqn. 7. With the calculatedh_(l)(x,z)'s, Eqn. 11 gave weightings over k_(x)-k_(z), which in turndetermined RF pulse waveforms. The resulting excitation profile andaverage SAR were compared to that of the first simulation study.

A discussion of the results of the above-described experiments follow.Focused excitation of a 5 cm by 5 cm region centered at x=8 cm and z=0inside the slab object was investigated in the first simulation study.Based on a body transmit coil, a reference, design employed pulses thattraversed 57 k_(x)=constant lines at Δ_(kx)=1/31.6 cycles/cm. Thex-direction localization that resulted from this reference design isshown in FIGS. 4-7. A parallel excitation design accomplished the 2Dlocalization task with the transmit coil array. Representing a 4-foldacceleration, the design employed pulses that traversed 14k_(x)=constant lines at Δ_(kx)=1/7 cycles/cm. U_(kx,4)(mΔ_(kx)) andU_(kx,7)(mΔ_(kx)), the k_(x)-direction weighting contributed by thecoils positioned at x=−4 cm and x=8 cm, respectively, are illustrated inFIG. 5 and FIG. 6. Localization along x due to each of the nine coils isshown in FIG. 7. Note that while the first aliasing side lobes were 4.5times closer to the target (center-to-center spacing=7 cm) as a resultof the sampling density reduction, the net amplitudes of these as wellas other aliasing lobes located inside the 40 cm FOV were negligible dueto incoherent addition, as shown in FIG. 4. Compared to the result ofthe body-coil approach, localization of the parallel excitation was aswell refocused (the imaginary component, not shown, was negligible) andof comparable spatial resolution. See FIG. 4.

In the phantom study, effects of incoherent addition on aliasing sidelobes were the focus of investigation. To this end, 2D excitation pulseswere designed to target a region in the water phantom directly below thecenter element. To facilitate the investigation, pulse calculationsfurther assumed an extended linear array instead of the 9-element one.The designed pulses were 5.7 msec in length. For the center elementexperiment, FIG. 8 shows the applied RF pulse (magnitude and phase) aswell as G_(x) and G_(z), the gradient pulses identically executed in allthe experiments of the series. Removing the coil's sensitivity profilefrom the resulting image provided an estimate of the 2D transversemagnetization distribution induced by the element, as shown in FIG. 9.FIG. 10 illustrates the B₁/sensitivity maps used. As a reference, FIG.11 illustrates the transverse magnetization distribution from anonselective excitation in a body-coil transmit-receive experiment.Noticeable in FIG. 9 is a noise amplification effect due to the divisionoperation employed for sensitivity profile removal, which tends toincrease in severity farther away from the sensitive region. To preventexcessive noise amplification from obscuring the investigation, thedivision operation was suppressed in distant regions.

Results from all nine experiments are summarized in FIG. 12, whichdisplays in rows 1 through 9 the mapped transverse magnetizationcorresponding to each of the experiments. The bottom row (row 10)presents the result of superimposing the individual maps, intended as aprediction of the result of a corresponding parallel excitation. Again,substantial reduction of aliasing side lobes due to incoherent additionwas observed. With the setup, contributions from the elements in theestablishment of the main lobe and the suppression of the aliasing lobeswere readily appreciated. The results from the center element alone andfrom the middle five and middle nine elements, suggest that localexcitation profile control is mainly achieved through nearby coils. Useof the extended array assumption in the pulse calculations accounted formuch of the residual aliasing (incomplete annihilation) towards the9-element array's boundary. Augmenting the array with elements beyondthe nine can rectify this effect. Designing pulses for the 9-elementarray can rid this effect too, in which case boundary coils' weightingwould experience the greatest changes.

2D parallel excitation pulses for a wrap-around array were designed andevaluated. The simulations concentrated on the task of selectivelyexciting an arbitrarily positioned local volume within a 40 cm-by-23 cmaxial field-of-view. Eqn. 7 was solved repeatedly based on the effectiveB₁ field patterns and an EPI trajectory comprising 14 k_(x)=constantlines at Δ_(kx)=1/6.9 cycles/cm. For the lth coil, l=1, 2, . . . , 7,the product of the desired 2D localization profile with the calculatedh_(l)(x,y) was then Fourier transformed to derive the coil's k-spaceweighting and RF pulse waveform by the parallel excitation. The netresult was substantially free of aliasing side lobes and represents anexcellent match to that of a reference excitation, which involvedbody-coil transmission of a 4-times longer conventional RF pulse.

The design of the last simulation study resulted in parallel excitationpulses that differed in shape from the pulses of the first simulationstudy. FIGS. 13-16 present the outcome with a format similar to that ofFIGS. 4-7. While the pulses maintained the same level of localizationaccuracy and spatial resolution as that of the pulses of the firstsimulation study, FIG. 13, the design changes led to a 38% reduction inaverage SAR, confirming the substantial impact of the integrated SARmanagement scheme.

With the present invention, designed RF pulses are synthesized,amplified and fed to corresponding transmit elements in parallel toinduce both spatial and temporal variations of the composite B₁ field,which, accompanied by appropriate gradient changes played out insynchrony, create a desired excitation profile upon completion ofexcitation. This is in contrast to a conventional approach, where thedesign of coil geometry and the offsets of driving-port phase/magnitudetarget B₁-field spatial homogeneity, and an RF pulse played duringexcitation is limited to manipulate B₁-field temporal variation only.One skilled in the art will recognize that inducing appropriate B₁spatiotemporal variations for excitation bears significant ramificationson RF excitation performance. That is, parallel excitation accommodatesexcitation acceleration and/or SAR control without substantial sacrificein the accuracy of producing the desired excitation profile.

In summary, the RF pulse driving a transmit element can be calculatedwith the Fourier transform of a spatially weighted version of thedesired excitation profile, the capacity for acceleratingmulti-dimensional excitation by the means of k-space sampling densityreduction lies with the suppression of aliasing lobes and can beachieved by appropriately designed driving pulses (spatial-frequencydomain weightings), and SAR management can be accomplished by minimizinga quadratic function in the driving sources, which searches a way oforchestrating the sources to achieve a desired excitation profile and/oracceleration while inducing an E field with minimum ensuing RF powerdeposition.

From an application perspective, fast imaging is an area where thepresent parallel excitation approach is particularly applicable. Undercircumstances where the anatomy of interest is contained in a localregion for example, multi-dimensional excitation that “spotlights” theregion allows acceleration of imaging by alleviating the burden ofspatial encoding inflicted on signal acquisition. Representingimprovements over conventional excitations, multi-fold shorter parallelexcitations support imaging volume definition/steering while breakingthe time cost barrier that hindered the practical use ofmulti-dimensional pulses in the past. Compared to the use of a parallelacquisition approach, focused imaging based on the parallel excitationapproach is not subject to the unique SNR degradation described by thegeometric factor. Combined use of the two approaches is possible and canprovide an even greater capacity for scan time reduction. While theexperiments reported here focused on 2D localization, the parallelexcitation approach applies to the creation and acceleration of general2D excitation profiles, with utilities including correction for fieldimperfection-induced effects and non-Fourier spatial encoding. Thepresent invention is also applicable to 3D excitations.

In high field imaging, the transmit system and driving means describedmay also be used to both manage excitation profile and regulate RF powerdeposition. Embodying an integrated treatment of excitation pulses andtransmit coils, the present invention facilitates excitation profilecontrol. Transmission with a distributed parallel system, accelerationof excitation and management of SAR further provides a solution to powerdeposition at high field strength.

The present invention further provides a method of MR imaging thatincludes determining a desired RF excitation profile and independentlydriving each transmit coil of a transmit coil array such that the resultof a collective excitation generated by the transmit coil arraysubstantially matches the desired RF excitation profile. As describedwith respect to FIGS. 2 and 3, each transmit coil is connected to adedicated RF amplifier that is designed to control RF excitation of thecorresponding transmit coil. More particularly, each RF amplifier orother control means provides a control signal representing an RF pulsewaveform specific to a corresponding transmit coil such that a compositeRF excitation is generated across an imaging volume that coincides withthe desired RF excitation profile. The method further includesdetermining the RF pulse waveform for each transmit coil from aspatially weighted version of the desired RF excitation profile. Asmentioned previously, the spatial weighting of each transmit coil isconsidered such that mutual coupling between the coils of the transmitcoil array is taken into account.

The present invention is also directed to an MRI apparatus that includesan MRI system having a magnet to impress a polarizing magnetic field, aplurality of gradient coils positioned about the bore of the magnet toimpose a magnetic field gradient, and a RF transceiver system and an RFswitch controlled by a pulse module to transmit RF signals to an RF coilassembly to acquire MR images. The MRI apparatus also includes acomputer programmed to design a plurality of RF pulse waveformsconfigured to control RF generation by a transmit coil array such thatthe result of collective RF generation across an imaging volumesubstantially matches a desired RF excitation profile independent oftransmit coil geometry. The computer is also programmed to determine aneffective spatial weighting imposed on the collective RF generation byeach transmit coil of the transmit coil array and apply the plurality ofRF pulse waveforms such that coupling induced inter-coil correlationsare taken into account. The effective spatial weighting imposed by eachtransmit coil includes spatial-frequency weightings induced by RFsources configured to control RF excitation of the transmit coils,weighting associated with mutual coupling between the transmit coils ofthe transmit coil array, as well as a respective B₁ field for eachtransmit coil of the array. The computer is also programmed to designthe plurality of RF pulse waveforms given any transmit coil array, assuch, the transmit coils may be linearly arranged, arranged in awrap-around fashion, or any other arrangement that may be implemented.Additionally, one or more of the transmit coils may also be designed toreceive MR signals.

The present invention may also be embodied in a computer readablestorage medium having a computer program stored thereon and representinga set of instructions that when executed by a computer causes thecomputer to control RF transmission by a plurality of transmit coils ofa transmit coil array such that spatial and temporal variation in acomposite B₁ field induces a desired excitation profile upon completionof RF transmission. The set of instructions further causes the computerto control application of gradients in an imaging volume to be insynchrony with spatial and temporal variation creation in the RFtransmissions. The set of instructions further causes the computer tocontrol application of control signals to the plurality of transmitcoils such that RF excitation by the plurality of transmit coils occursin parallel. The computer is also caused to determine the spatial andtemporal variations to be induced with at least one transmit coil'seffective B₁ field map. The effective B₁ field maps for each transmitcoil reflect mutual coupling of the plurality of coils. Preferably, theeffective B₁ field maps are generated during calibration of the transmitcoil array.

The present invention has been described in terms of the preferredembodiment, and it is recognized that equivalents, alternatives, andmodifications, aside from those expressly stated, are possible andwithin the scope of the appending claims.

1. A method of MR imaging comprising the step of independently drivingeach transmit coil of a transmit coil array such that a collectiveexcitation generated by the transmit coil array substantially matches adesired RF excitation profile.
 2. The method of claim 1 wherein the stepof independently driving includes the step of separately controllingcurrent generated in each transmit coil by a respective RF amplifierconnected thereto.
 3. The method of claim 2 wherein the step ofseparately controlling includes the step of providing a control signalto each RF amplifier, each control signal representing an RF pulsewaveform specific to a corresponding transmit coil.
 4. The method ofclaim 3 further comprising the step of determining the RF pulse waveformfor each transmit coil from a spatially weighted version of the desiredRF excitation profile.
 5. The method of claim 4 further comprising thestep of determining a spatial weighting for each transmit coil thattakes into account at least mutual coupling between the transmit coils.6. The method of claim 5 wherein the spatial weighting for each transmitcoil further takes into account spatial frequency sampling induced bythe pulsing gradient field and spatial weightings induced by each coil'sB₁ field.
 7. An MRI apparatus comprising: a magnetic resonance imaging(MRI) system having a magnet to impress a polarizing magnetic field, aplurality of gradient coils positioned about the bore of the magnet toimpose a magnetic field gradient, and an RF transceiver system and an RFswitch controlled by a pulse module to transmit RF signals to an RF coilassembly to acquire MR images; and a computer programmed toindependently control RF generation by each coil of a transmit coilarray such that a collective RF generation across an imaging volumesubstantially matches a desired RF excitation profile.
 8. The MRIapparatus of claim 7 wherein the computer is further programmed todetermine an effective spatial weighting imposed on the collective RFgeneration by each transmit coil of the transmit coil array and design aplurality of RF pulse waveforms such that coupling-induced inter-soilcorrelations are taken into account.
 9. The MRI apparatus of claim 8wherein the effective spatial weighting imposed by each transmit coilincludes at least spatial-frequency weightings induced by independentlycontrolled RF sources connected to the transmit coil array, weightingassociated with mutual coupling between the transmit coils of thetransmit coil array, and a respective B₁ field.
 10. The MRI apparatus ofclaim 8 wherein the plurality of RF pulse waveforms are furtherconfigured to effect shorter time-span execution k-space traversing byreducing excitation k-space sampling density.
 11. The MRI apparatus ofclaim 7 wherein the computer is further programmed to control RFgeneration such that the collective RF generation substantially matchesthe desired excitation profile independent to transmit coil arraygeometry.
 12. The MRI apparatus of claim 7 wherein the computer isfurther programmed to determine an effective B₁ field for each transmitcoil during calibration of the MRI system.
 13. The MRI apparatus ofclaim 7 wherein the transmit coil array is linearly arranged and furtherconfigured to receive MR signals.
 14. The MRI apparatus of claim 7wherein the transmit coil array is further configured to induce RF fieldbased on driving parallel excitation pulses.
 15. The MRI apparatus ofclaim 7 wherein the plurality of waveform are further configured toreduce aliasing side lobes in the collective RF generation across theimaging volume.
 16. The MRI apparatus of claim 7 wherein the computer isfurther programmed to design a plurality of RF pulse waveforms to beindependently applied to the transmit coil array.
 17. A computerreadable storage medium having a computer program stored thereon andrepresenting a set of instructions that when executed by a computercauses the computer to control RF transmission by a plurality oftransmit coils of a transmit coil array such that spatial and temporalvariation in a composite B₁ field induces a desired excitation profileupon completion of RF transmission.
 18. The computer readable storagemedium of claim 17 wherein the set of instructions further causes thecomputer to control application of gradients in an imaging volume to bein synchrony with spatial and temporal variation creation in the RFtransmissions.
 19. The computer readable storage medium of claim 17wherein the set of instructions further causes the computer to controlapplication of control signals to the plurality of transmit coils suchthat RF excitation by the plurality of transmit coils in parallel. 20.The computer readable storage medium of claim 17 wherein the set ofinstructions further causes the computer to determine the spatial andtemporal variations to be induced with at least one transmit coil'seffective B₁ field map.
 21. The computer readable storage medium ofclaim 20 wherein the effective B₁ field maps at least reflect mutualcoupling of the plurality of transmit coils.
 22. The computer readablestorage medium of claim 17 wherein the effective B₁ field maps aregenerated during calibration of the transmit coil array.
 23. Thecomputer readable storage medium of claim 17 wherein the set ofinstructions further causes the computer to determine control signals tobe applied to the plurality of transmit coils based on at least aFourier transform of a spatially weighted version of the desiredexcitation profile.
 24. The computer readable storage medium of claim 17wherein the set of instructions further causes the computer to controlRF transmission such that the composite B₁ field is createdthree-dimensionally about the imaging volume.